Operability analysis of nonlinear processes based on incremental dissipativity

Process operability can be defined as the ability of a process to reject disturbances at a specified operating point and/or to move quickly and smoothly from one operating point to another operating point using a feedback control system. Unlike linear processes, the properties of nonlinear processes (e.g., stability, minimum phase condition, etc.) are different around different equilibria. Most existing operability analysis for nonlinear systems focuses on one particular operating point of interest. This paper addresses the issues of dynamic process operability at various operating points, including the reachability of all equilibrium points or output trajectories in an operating region, regardless of initial conditions. In this work, a nonlinear analysis approach is developed based on the concept of incremental stability. Conditions for incremental stability are derived based on incremental dissipativity. The links between input and output multiplicities and incremental dissipativity are explored. The dynamic control performance achievable in terms of the speed of the response of the closed-loop system and offset minimization is studied. A method for determination of incremental dissipativity using Linear Differential Inclusion (LDI) is also presented, to facilitate the dissipativity based operability analysis.